Target Probability Modulates Fixation-Related Potentials in Visual Search

Abstract

This study investigated the influence of target probability on the neural response to target detection in free viewing visual search. Participants were asked to indicate the number of targets (one or two) among distractors in a visual search task while EEG and eye movements were co-registered. Target probability was manipulated by varying the set size of the displays between 10, 22, and 30 items. Fixation-related potentials time-locked to first target fixations revealed a pronounced P300 at the centro-parietal cortex with larger amplitudes for set sizes 22 and 30 than for set size 10. With increasing set size, more distractor fixations preceded the detection of the target, resulting in a decreased target probability and, consequently, a larger P300. For distractors, no increase of P300 amplitude with set size was observed. The findings suggest that set size specifically affects target but not distractor processing in overt serial visual search.

Introduction

Visual search is an essential part of everyday human behavior. When we look for our car keys, a familiar face in the crowd, or an icon on the computer screen, we perform a visual search, that is, we search for a target object among other objects (distractors). In a complex visual environment, we can only rarely spot the target right away. Instead, we have to attend to objects consecutively, a process termed serial visual search (Treisman & Gelade, 1980). In this article we investigate the electrophysiological response to targets when the number of distractors varies while participants perform a serial visual search that requires eye movements.

Visual search has attracted a great deal of research interest over the past decades (for a review, see Eckstein, 2011). The bulk of this research is relying on response time experimentation. Research using electroencephalography (EEG) has contributed to the understanding of brain activity during search on a high resolution time scale. This research has concentrated on search paradigms which preclude eye movements, so-called covert visual search (e.g., Hickey, Di Lollo, & McDonald, 2009; Luck & Hillyard, 1990, 1994) because eye movements affect the measured EEG (Plöchl, Ossandón, & König, 2012). Other studies used eye tracking to trace overt shifts of attention, i.e. eye movements, but did not measure brain activity (see Findlay & Gilchrist, 2003, for a review).

Recent advances in eye tracking technology and EEG analysis methods have opened the door to investigate neural correlates of visual perception and cognition under more natural conditions. Co-registration of EEG and eye movements is a promising technique in this regard, which offers the opportunity to study brain activity in unrestricted viewing behavior. As opposed to the conventional analysis where EEG is time-locked to an externally presented stimulus, here eye movements themselves serve as natural markers to segment ongoing EEG activity. EEG can be time-locked to certain ocular events, such as the onset of fixations or saccades (fixation-related potentials, FRPs, or saccade-related potentials, SRPs).

To date, FRPs have been studied in various research areas, including word recognition and reading (Baccino & Manunta, 2005; Dimigen, Sommer, Hohlfeld, Jacobs, & Kliegl, 2011; Frey et al., 2013; Henderson, Luke, Schmidt, & Richards, 2013; Hutzler et al., 2007; Simola, Holmqvist, & Lindgren, 2009), object recognition (Rämä & Baccino, 2010), free picture viewing (Fischer, Graupner, Velichkovsky, & Pannasch, 2013; Graupner, Pannasch, & Velichkovsky, 2011; Graupner, Velichkovsky, Pannasch, & Marx, 2007), change detection (Nikolaev, Jurica, Nakatani, Plomp, & van Leeuwen, 2013; Nikolaev, Nakatani, Plomp, Jurica, & van Leeuwen, 2011), natural scene viewing (Dandekar, Privitera, Carney, & Klein, 2012; Simola, Le Fevre, Torniainen, & Baccino, 2015; Simola, Torniainen, Moisala, Kivikangas, & Krause, 2013), navigation in a virtual environment (Jangraw, Wang, Lance, Chang, & Sajda, 2014), and visual search (Brouwer, Hogervorst, Oudejans, Ries, & Touryan, 2017; Brouwer, Reuderink, Vincent, van Gerven, & van Erp, 2013; Devillez, Guyader, & Guérin-Dugué, 2015; Dias, Sajda, Dmochowski, & Parra, 2013; Finke, Essig, Marchioro, & Ritter, 2016; Kamienkowski, Ison, Quiroga, & Sigman, 2012; Kaunitz et al., 2014; Körner et al., 2014; Ries, Touryan, Ahrens, & Connolly, 2016; Seidkhani et al., 2017; Touryan, Lawhern, Connolly, Bigdely-Shamlo, & Ries, 2017; Ušćumlić & Blankertz, 2016; Wenzel, Golenia, & Blankertz, 2016).

EEG analysis in free viewing bears several methodical problems. Besides distortions caused by ocular artifacts, one of the major challenges is the temporal overlap of EEG responses evoked by subsequent eye movements. Due to the fast succession of fixations and saccades in unrestricted viewing, eye movement events follow each other within 300 ms or less. Moreover, certain eye movement characteristics directly affect the FRPs (for a detailed description, see Nikolaev et al., 2016). The most influential eye movement characteristic is saccade size which correlates positively with the amplitude of a potential caused by contraction of the extraocular muscles at saccade onset, the so-called saccadic spike potential. Saccade size also affects a potential that occurs approximately 100 ms after fixation onset, the lambda wave (Dimigen et al., 2011; Keren, Yuval-Greenberg, & Deouell, 2010; Nikolaev, Meghanathan, & van Leeuwen, 2016; Plöchl et al., 2012). Systematic differences in eye movement characteristics thus act as potential confounds and require careful control (Dimigen et al., 2011; Nikolaev et al., 2016). Therefore, early EEG- and eye movement co-registration studies focused on the saccadic spike and lambda potential using controlled saccadic tasks (e.g., Kazai & Yagi, 1999, 2003; Thickbroom, Knezevič, Carroll, & Mastaglia, 1991; Thickbroom & Mastaglia, 1986). More recent investigations have shown, however, that it is possible to obtain longer-latency FRP components which provide insight into cognitive mechanisms even in unrestricted eye movement behavior.

In visual search tasks, for example, Kamienkowski et al. (2012) have demonstrated that FRPs allow to distinguish between fixations on targets and on distractors (see also Brouwer et al., 2017, 2013; Dandekar et al., 2012; Devillez et al., 2015; Dias et al., 2013; Finke et al., 2016; Kamienkowski et al., 2012; Kaunitz et al., 2014; Körner et al., 2014; Ries et al., 2016; Touryan et al., 2017; Ušćumlić & Blankertz, 2016; Wenzel et al., 2016). The detection of a target in visual search elicits a positive FRP component similar to the P300 evoked by rare target stimuli in a classical visual oddball task (Kamienkowski et al., 2012; Kaunitz et al., 2014). This P300 activity can discriminate fixations on targets from fixations on non-targets on a single-trial basis (Brouwer et al., 2017, 2013; Jangraw et al., 2014; Kaunitz et al., 2014; Ušćumlić & Blankertz, 2016; Wenzel et al., 2016). Components resembling a P300 have been reported for abstract stimuli such as letters or colored bars (e g., Dias et al., 2013; Kamienkowski et al., 2012; Ries et al., 2016), faces (Kaunitz et al., 2014), and objects in natural scenes, depicting everyday life situations such as looking for a kitchen item (Dandekar et al., 2012; Devillez et al., 2015). This suggests that the fixation-related P300 reflects top-down processing of objects relevant to the current behavioral goal.

The majority of the aforementioned FRP studies have focused on discrimination between targets and distractors. However, some studies have further characterized the P300 and its role in target detection, e.g., by identifying factors that modify the P300. For instance, it was found to be affected by the dynamics of target appearance, depending on whether stimuli pop up, smoothly fade in, or move into the screen (Ušćumlić & Blankertz, 2016), target saliency (Wenzel et al., 2016), or workload imposed by concurrent task demands (Brouwer et al., 2017; Ries et al., 2016; Touryan et al., 2017). Those findings shed light on the not well understood properties and functional significance of the P300 in free viewing.

One central aspect of visual search is that the target always constitutes a rare event among the distractors. This rarity (or low probability) of the target is likely a key condition for eliciting the fixation-related P300. However, the ratio of targets to distractors, and thus the role of target probability in visual search tasks with unrestricted eye movement behavior, has not been addressed previously. In this paper we seek to characterize this dependency of the P300 on target probability.

The traditional EEG literature which has used the oddball paradigm to study properties of the P300 suggests that target probability is a major determinant of the P300 (for reviews see Kok, 2001; Picton, 1992; Polich, 2007, 2012). A target in serial visual search represents a rare event among distractors, similarly to the oddball task where an infrequent deviant (or target) is presented within a sequence of standard stimuli (distractors; Donchin, 1981; Donchin & Coles, 1988). A well-established finding in oddball tasks is that P300 amplitude increases as target probability decreases (Duncan-Johnson & Donchin, 1977, 1982; Polich & Bondurant, 1997; Polich, Brock, & Geisler, 1991). The P300 is sensitive not only to overall probability of targets in an experiment but also to local target probability, i.e., the number of distractors immediately preceding the target (Duncan-Johnson & Donchin, 1977, 1982; Gonsalvez et al., 1999; Gonsalvez, Barry, Rushby, & Polich, 2007; Squires, Petuchowski, Wickens, & Donchin, 1977; Squires, Wickens, Squires, & Donchin, 1976). Correspondingly, in visual search the neural response to a target may depend on the number of non-target objects (or distractors) inspected before encountering a target.

Luck and Hillyard (1990) have argued that serial visual search bears a resemblance to the oddball task as it represents a sequence of decisions about stimulus identity. The detection of the target (resulting in a positive decision) is typically preceded by several negative decisions for distractors, rendering the target an improbable event which should elicit a P300. The authors hypothesized that P300 amplitude should thus increase with set size (the number of items in the display) because the number of preceding negative decisions increases as a function of set size. In an EEG search experiment without eye movements, they observed such an increase of P300 amplitude with set size in event-related potentials (ERPs).

The aim of this paper is to corroborate the previously reported distinction between target and distractors and furthermore to investigate the extent to which the target-related P300 itself is modulated by target probability. To our knowledge, the impact of target probability on the P300 has not yet been studied in overt visual search. Establishing and characterizing probability as a fundamental determinant of the P300 may represent a major step in further delineating the role of this component in visual search and free viewing.

We investigated the influence of target probability on the neural response to target detection in an overt visual search experiment, using simultaneous recordings of EEG and eye movements. Participants performed a visual search task where they were asked to indicate the number of targets (one or two) among distractors. To manipulate target probability, we varied the set size between 10, 22, and 30 items. We analyzed FRPs time-locked to the first target fixation, separately for each set size. First, we expected that target detection elicits a P300 component. Second, we hypothesized that P300 amplitude increases as a function of set size, because as set size increases, more distractor fixations precede the detection of the target, rendering it a rarer event. To validate that set size specifically influenced target but not distractor processing, we conducted a control analysis on the distractor FRPs. We hypothesized that distractors FRPs should not show an amplitude modulation with regard to set size and not elicit a P300.

Method

Participants

Fourteen healthy participants (university students, 9 female, 13 right-handed) took part in the experiment (mean age 26.4 years, SD = 3.1). They had normal or corrected-to-normal vision (contact lenses) and disavowed any history of neurological or psychiatric disease. They received a monetary compensation or course credit and gave written, informed consent to participate in the study. The study was approved by the ethics committee of the University of Graz.

Design and Stimuli

Participants performed a multiple-target visual search for ”T”s presented as target letters amongst ”L”s as distractor letters. Each display contained either one target or two targets. The number of items in the search displays (set size) varied between 10, 22, and 30 items.

The letters were presented in gray on black background. The width of a single letter was 0.25° of visual angle at a viewing distance of approximately 71 cm. Letters were surrounded by a gray circle with an outer diameter of 0.8° and a line thickness of 0.16°. The circle provided a clear target for saccade planning while reducing the ability to identify the letters in peripheral vision (Körner & Gilchrist, 2007). The items appeared randomly at the intersection of an imaginary 4 × 4, 6 × 6 or 7 × 7 grid for set sizes with 10, 22, or 30 items, respectively. The size of a grid cell was 3.4°. The center of the letter deviated randomly from the intersection by ± 0.2° both in horizontal and vertical direction. The whole viewing area subtended 13.6° ×13.6°, 20.4° × 20.4°, and 23.8° × 23.8° for set sizes 10, 22, and 30, respectively (see Figure 1 for an example of the 10-item display).

Figure 1.

Example of a 10-item search display with two targets (T) and eight distractors (L). Stimuli were presented in gray on black background. The figure is not true to scale; the exact dimensions are given in the Methods section.

In a pilot experiment we had found that these dimensions kept the “density” of the displays (i.e., the number of items per area) approximately constant across set sizes. When we visually compared the normalized frequency distributions of saccade amplitudes of the main experiment we found that they were virtually identical across set sizes. They showed three clearly pronounced peaks, a first one for saccades in the range around 0.9°, denoting correctional (and micro-) saccades. The maximum of the distribution was located at around 3.9° which coincided with the distance where two neighbouring letters would be located in the imaginary grid. The third peak was located in the range of 8.0° which is about twice that size. The similarity of the distributions between set sizes was confirmed by three two-sample Kolmogorov-Smirnov tests (all ps > .23). The comparableness of saccade distributions is important because the saccade amplitude correlates with the magnitude of the saccadic spike potential and the lambda wave (e.g., Nikolaev et al., 2016).

Task and Procedure

Participants were seated in an acoustically and electrically shielded, dimly lit cabin in front of a monitor. Before the main experiment, participants performed 10 practice trials. Afterwards, a short pre-experimental procedure was conducted where participants performed four different eye movement tasks: blinks, vertical saccades and blinks, vertical saccades, and horizontal saccades (4 trials per task with 15 s duration each). This procedure was carried out to collect additional eye movement data for the ICA-based correction of oculomotor artifacts (Dimigen et al., 2011; Keren et al., 2010; Plöchl et al., 2012).

Each trial of the main experiment started with the presentation of a fixation disc in the center of the screen that was used for the drift correction by the eye tracker. Once the fixation on the disc was registered by the experimenter, the screen was cleared. After a delay of ~200 ms, the search display was presented. Participants were asked to decide whether there were one or two targets in the display and to press a corresponding button. They were instructed to give the one-target response with the left hand and the two-target response with the right hand on a gamepad, and to respond as quickly and as accurately as possible. With the button press the screen was cleared and the trial ended. After an inter-trial interval of 900 ms, the next trial started.

The whole experiment consisted of six blocks with 60 trials each, separated by short breaks. Trial order was randomized across participants with an equal number of one- and two-target trials, and an equal number of 10, 22, and 30 item displays per block (10 trials per set size for each target condition within each block). In total, we collected 360 trials for each participant.

Eye Movement and EEG Recording

Eye movements were recorded with an EyeLink 1000 eye tracker (SR Research, Canada) using the desktop mount (remote) setup. Participants’ head movements were stabilized by a chin and forehead rest. Eye movements were recorded monocularly with 1000 Hz sampling rate. The eye tracker was calibrated at the beginning of each block with a 9-point calibration procedure. Initially, both eyes were calibrated and eye movements were then recorded from the eye with the better spatial resolution (avg. error < 0.35°). The procedure was controlled by a presentation computer attached to the eye tracker via an Ethernet connection. The control software was custom-written in C++ using code from SR Research (Canada). Displays were presented on a 24-inch TFT monitor with a native resolution of 1920 x 1200 pixels at 60 Hz.

EEG was recorded from 59 Ag/AgCl electrodes placed according to the international 10-20 system using a standard electrode cap (EasyCap GmbH, Hersching, Germany). EOG was measured from three electrodes located at the outer canthi of the eyes and above the nasion. All electrodes were referenced to the right mastoid. An additional channel was recorded from the left mastoid in order to re-reference the data offline. The ground electrode was located at the collarbone. Signals were digitized with 500 Hz sampling rate with BrainAmp amplifiers (Brain Products GmbH, Munich, Germany). EEG and EOG signals were band-pass filtered online between 0.01 – 100 Hz, and a 50 Hz notch filter was applied. Impedances were kept below 5 kΩ. To synchronize EEG and eye movement recordings, the stimulus presentation computer sent synchronization messages to the eye tracker via the Ethernet link and trigger pulses (TTL) to the EEG recording system via the parallel port at the start (after the drift correction) and end of each trial.

Data Processing and Analysis

Data were processed with MATLAB R2015b (The MathWorks Inc, Natick, MA, USA) and the EEGLAB toolbox 13.6.5b (Delorme & Makeig, 2004), with the EYE-EEG 0.41 (Dimigen et al., 2011) and ERPLAB 5.0.0 extensions (Lopez-Calderon & Luck, 2014). EEG and eye tracking data were imported into EEGLAB and synchronized based on the common online triggers using the EYE-EEG plugin.

Eye movement detection and processing

Eye movements were detected using the velocity-based detection algorithm (Engbert & Mergenthaler, 2006), provided within the EYE-EEG plugin. As parameters, a velocity threshold of 6 median-based standard deviations, minimum saccade duration of 4 ms, and minimum inter-saccadic interval of 50 ms were defined. Fixations were defined as intervals between saccades.

Fixation pre-processing

Each fixation made between display onset and button press response was assigned to individual items of the search display. For each fixation we computed the Euclidean distance between the current fixation and each item in the display of the given trial. The fixation was attributed to the item with the smallest distance.

Only correct trials, where at least one target fixation was registered, were analyzed further. For every trial, the number of fixations until the manual response was counted. Immediate re-fixations of an item were ignored, that is, if two or more fixations on the same item without intermediate fixation of another item occurred in succession, only the first was counted. For each fixation we also determined the fixation rank, that is, the number of fixations from the display onset until the current fixation (serial position in the scan-path).

Selection of target fixations for FRP analysis

For FRP analysis, fixation events of interest were selected in order to create later the EEG epochs time-locked to the fixation onset (-200 to +600 ms, see EEG processing and analysis). For every trial, we identified the first fixation on the target. We used only the first of two targets because EEG in the related fixation interval was free of possible contamination due to preparation of the manual response. The following exclusion criteria were then applied to these first target fixations: To preclude cases where the moment of target processing was uncertain, we excluded fixations followed by an immediate re-fixation (i.e., two or more subsequent fixations on the same target without intermediate fixation of another item). To avoid contamination of the FRPs with the visual potential evoked by display onset, we also removed fixations within the first 700 ms after display onset (Dimigen et al., 2011). Fixations were further excluded if the epochs contained a manual response, blinks or EEG artifacts (as described below). Although the manual response was delayed relative to the target, it could in rare occasions occur within the epoch limits if the target was found late during search. This selection procedure resulted in an average number of 189.36 (SD = 39.85) target epochs per participant, corresponding to an average of 52.62 % (SD = 11.08 %) of 360 trials. The average number of final target events for each set size per participant is presented in Table 1.

Table 1. Average number and range of final target and fixation rank-matched distractor events for each set size.

	Size 10	Size 22	Size 30
Targets	58.86 (12.58) / 35-81	62.57 (14.58) / 37-78	67.93 (16.17) / 40-90
Distractors	56.86 (12.93) / 30-79	62.57 (14.58) / 37-78	67.86 (16.14) / 40-90

Note: Numbers in parentheses denote SD, numbers after the slash the range.

Selection of distractor fixations for FRP analysis

To evaluate if set size specifically influences the processing of targets but not distractors, we selected a set of suitable distractor fixations that were matched to the target fixations with respect to their fixation rank. This approach ensured that distractors and targets were from the same serial position in the scan-path. It was expected that the manipulation of set size would lead to a systematic difference in the number of items inspected before finding the first target (i.e., a higher target fixation rank for larger set sizes). We hypothesized that target probability varies with target fixation rank, consequently modulating the target-related P300. It was therefore important to show that the fixation rank alone does not explain potential differences in the FRPs. The analysis of rank-matched distractors also served the purpose of controlling for such an effect of fixation rank.

In a first step, a subset of distractor fixations was selected by applying the same exclusion criteria as for target fixations. In addition, distractor EEG epochs were discarded if they contained the onset of a target fixation or temporally overlapped with a target epoch. Then, for every target, a fixation-rank matched distractor from a different trial with the same set size was drawn randomly from the available subset (pre-selected in the previous step). Each distractor could be selected only once as a match for a target. When a distractor was chosen, temporally adjacent distractors from the same trial, whose epochs would overlap with the current one, were excluded and not considered further for matching.

By this routine, we obtained three subsets of distractor fixations (one for each set size) matching the fixation rank characteristics of the targets. For a small number of targets, no rank-matched distractor could be found, resulting in a slightly smaller number of distractor than target epochs (Table 1).

EEG processing and analysis

EEG and EOG data were re-referenced to linked mastoids and high-pass filtered at 1 Hz (-6 dB cut-off frequency) using a non-causal zero-phase windowed sinc FIR filter (1 Hz transition bandwidth, 60 dB stopband attenuation, order 1812, Kaiser window). After removal of inter-trial intervals (including the time of the drift correction), EEG data were visually inspected for non-stereotypical artifacts (e.g., muscle activity, body movement, electrode jumps, swallowing) and the affected segments were discarded. The remaining data segments from all trials and the pre-experimental session with extensive eye movement were then concatenated.

Independent component analysis (ICA; Makeig, Bell, Jung, & Sejnowksi, 1996) was used to remove ocular artifacts and noisy channels. The pre-processed datasets of each participant containing both EEG and EOG were decomposed into 62 independent components (ICs) using the Extended Infomax algorithm (Lee, Girolami, & Sejnowski, 1999). To identify ICs representing eye movement-related artifacts, we applied the variance-ratio criterion suggested by Plöchl et al. (2012), using integrated information from the eye tracker. This criterion compares the variance of each IC activation during saccade intervals with the variance during fixations. If the ratio for a respective IC exceeded a threshold of 1.1, the IC was classified as eye-movement related. On average, we identified 3.36 such ICs per participant (range: 3-4 ICs). In addition, individual ICs were evaluated by visual inspection, considering the IC scalp map, activation (time series) and power spectral density. Based on focal topography, noisy time course, and increased power in the high-frequency range, we identified ICs representing bad channels and marked them for later rejection. We classified as such on average 3.22 ICs (range: 2-6) in nine participants.

High-pass filtering is an important prerequisite for ICA because slow drifts in the data introduce spatial non-stationarities (Debener, Thorne, Schneider, & Viola, 2010; Winkler, Debener, Müller, & Tangermann, 2015). Such drifts can have adverse effects on ICA and result in a poor separation of components (Winkler et al., 2015). Therefore, high-pass filtering with a cut-off at around ~1 Hz is a recommended step preceding ICA (Debener et al., 2010). On the other hand, it is recommended to restrict the cut-off to a maximum of 0.1 Hz for ERP analysis (Luck, 2014; Tanner, Morgan-Short, & Luck, 2015). A possible solution to this problem is to train the ICA on data high-pass filtered with 1 Hz and apply the obtained ICA weights to the original or differently filtered data (see Debener et al., 2010; Hyvärinen, Karhunen, & Oja, 2001; Widmann, Schröger, & Wetzel, 2018; Winkler et al., 2015).

Hence, for the FRP analysis we generated a copy of the original data and applied 0.1 Hz high-pass and 30 Hz low-pass filters (ERPLAB zero-phase Butterworth filter, order 4, 24 dB/oct). In any other respects, the pre-processing was identical to the procedure described before. The ICA weights obtained in the previous step were then applied to this dataset and the previously identified ocular artifact and bad channel ICs were rejected. All further analyses used these ICA-corrected data.

To obtain FRPs, the cleaned data were segmented into epochs relative to fixation onset, ranging from 200 ms before to 600 ms after fixation onset. Subsequently, FRPs were baseline corrected using the baseline interval from -200 to -100 ms. This baseline has been used in prior FRP studies (Devillez et al., 2015; Kamienkowski et al., 2012; Kaunitz et al., 2014; Ries et al., 2016). Since EEG in this interval may be affected by the preceding saccade size and fixation duration (Nikolaev et al., 2016), we tested these eye movement characteristics for absence of a difference between set sizes, as we will report below. The FRP epochs were averaged for each participant for each set size, and for targets and distractors separately.

Statistical Analysis

Statistical analyses were performed with Statistica13 (StatSoft GmbH, Hamburg, Germany). In all ANOVAs, sphericity assumption was tested with Mauchley’s sphericity test. In case of violations, degrees of freedom were corrected by means of the Greenhouse-Geisser procedure and corrected degrees of freedom and p-values are reported. To follow up on significant main effects or interactions revealed by the ANOVAs, for pairwise comparisons the Newman-Keuls post-hoc test was used.

Results

Behavioral and Eye Movement Results

Participants made only 4.09 % (SD = 2.39) errors, on average. Error rates were slightly higher in the two-target search than in the one-target search because the probability of missing a target is higher in the two-target search (Table 2). The following behavioral and eye movement measures were evaluated with 2 × 3 repeated measures ANOVAs with the within-subject factors Set Size (10, 22, 30) and Number of Targets (one-target and two-target search). Manual response time (RT) and average number of fixations per trial increased as a function of set size (Table 2). The more items in the display, the longer took the search and the more eye movements were made (Set Size: F(1.13, 14.65) = 342.39, p < .001, η_p² = 0.96, and F(1.25, 16.22) = 720.16, p < .001, η_p² = 0.98). RTs and number of fixations were higher in the one-target than in the two-target search (Number of Targets: F(1,13) = 83.81, p < .001, η_p² = 0.87 and F(1,13) = 107.76, p < .001, η_p² = 0.89). Participants needed more time and more fixations in the one-target search as they had to inspect all items (exhaustive search), as opposed to the two-target search which could be aborted as soon as the second target was found (self-terminating search). RTs and number of fixations increased with set size to a greater extent in the one-target than in the two-target search (Set Size × Number of Targets:F(1.34, 17.45) = 64.29, p < .001, η_p² = 0.83 and F(2,26) = 91.51, p < .001 η_p² = 0.88).

Table 2. Behavioral and eye movement results for each target condition and set size for correct trials (upper panel) and for the final subset of target fixations for FRP analysis (lower panel).

	One Target			Two Targets
	Size 10	Size 22	Size 30	Size 10	Size 22	Size 30
Error rate (%)	0.48 (1.38)	0.60 (1.06)	0.60 (1.06)	3.93 (3.18)	8.23 (6.95)	10.72 (7.78)
Response time (ms)	4007 (776)	8334 (1668)	11118 (2328)	2918 (391)	5387 (693)	7332 (1000)
Number of fixations per trial	12.38 (1.93)	26.53 (4.23)	35.31 (5.29)	8.50 (0.74)	16.81 (1.01)	22.91 (1.66)
Time until target fixation (ms)	1614 (175)	3344 (353)	4865 (796)	990 (181)	2073 (216)	2994 (511)
Fixation rank	5.88 (0.41)	11.76 (1.04)	16.59 (1.59)	3.72 (0.49)	7.50 (0.49)	10.47 (1.19)
Time until target fixation (ms)	1842 (206)	3501 (523)	5191 (849)	1453 (134)	2557 (375)	3397 (536)
Fixation rank	6.65 (0.50)	12.35 (1.73)	17.74 (1.99)	5.30 (0.41)	9.18 (1.08)	11.88 (1.29)

Note: Numbers in parentheses denote SD.

Similarly, the time and the number of fixations from display onset until the detection of the first target (fixation rank) increased as a function of set size (Set Size: F(1.29, 16.74) = 411.38, p < .001, η_p² = 0.97, and F(2,26) = 890.71, p < .001, η_p² = 0.99). Search time and target fixation rank were higher in the one-target search than in the two-target search since the probability of finding a target earlier is higher the more targets are present among distractors (Number of Targets: F(1,13) = 192.71, p < .001, η_p² = 0.94 and F(1,13) = 234.89.71, p < .001, η_p² = 0.95). For both measures, the increase with set size was larger in the one-target than in the two-target search (Set Size × Number of Targets: F(1.20, 15.54) = 29.42, p < .001, η_p² = 0.69 and F(1.30, 16.95) = 34.05, p < .001, η_p² = 0.72; Table 2). These results confirm that, with increasing set size, a larger number of distractor fixations preceded the first detection of the target, decreasing the local probability of the target.

The results reported above were obtained for all correct trials. Since the first target fixations selected for the FRP analysis (see Selection of target fixations for FRP analysis) represent only a subset of these trials, the time until target detection and fixation rank were analyzed for this subset separately. Both measures were, on average, slightly higher in the FRP subset (Table 2, lower panel) as compared to all trials because fixations of the target within 700 ms after display presentation were discarded (see Methods for details). However, for both measures the pattern of results was the same as for all target fixations: the significant effects of Set Size, Number of Targets and Set Size × Number of Targets interaction.

EEG Results

This section is divided into three parts: First, we report on the target FRPs, second, on the distractor FRPs, and third, on analyses performed to control for confounding effects of eye movements. We refrained from a direct comparison of targets and distractors because of systematic differences in eye movement characteristics as, for example, fixation durations on targets in comparison to distractors. Instead, we compare the FRPs between the set sizes for each item type separately. Eye movement characteristics were balanced across these conditions, as described in detail in the last part of the results.

Target FRPs

To evaluate the influence of set size on target processing, we compared FRPs time-locked to the onset of fixation on the first target. We observed a positive-going wave in the time range of 350-600 ms, resembling a P300 (Figure 2A/B). This response to targets was modulated by set size: A larger amplitude was observed in the FRPs for set sizes 22 and 30 than for set size 10. The amplitude did not differ between set size 22 and 30.

Figure 2.

A. Grand average FRPs time-locked to first target fixations for each set size on three midline channels (Fz, Cz, Pz). Time point zero denotes fixation onset. FRPs were baseline corrected using a baseline window of -200 to -100 ms prior to fixation onset. B. Topographical maps illustrating the mean amplitude at different time points in steps of 50 ms.

The time course of the FRPs was similar between set sizes up until the beginning of this late positive component. The P300 started to emerge around 350 ms following fixation onset and reached its peak at a latency of ~450 ms, corresponding to the typical time range of the P300 in the visual domain (Luck, 2014; Polich, 2012). On a descriptive level, differences between set sizes in the temporal characteristics and shape of the P300 were also observed. For the large set sizes, the P300 at Pz reached its peak slightly later and was more sustained than for set size 10 (size 10: 426 ms, size 22: 458 ms, size 30: 438 ms). The longer-lasting activity was also clearly visible in the spatial maps (Figure 2B, 550 ms).

The P300 showed the same spatial distribution for the three set sizes, suggesting that it can be considered the same component. In general, the positivity was widespread across the scalp, although most pronounced over midline electrode sites. The P300 started out over the main frontal and central regions and then spread to posterior locations, indicated by the spatial topographies as well as an earlier frontal (Fz) than parietal (Pz) peak. At peak latency, the P300 was observed over the centro-parietal cortex, resembling the topography of the classical P300 or “P3b” (Polich, 2007).

Statistical analysis focused on three midline channels (Fz, Cz, Pz) typically used to study the P300 in ERPs or FRPs (e.g., Devillez et al., 2015; Kaunitz et al., 2014; Polich, 2012). First, we determined the peak latency in the grand average FRP collapsed across set sizes and averaged across the three channels (430 ms). The mean FRP amplitude was then extracted separately from the FRPs for each set size for the three channels in a ±50 ms time window centered around this peak, i.e., from 380 to 480 ms after fixation onset (Table 3). The amplitude at Pz, for instance, increased from 6.18 μV for set size 10 to 8.19 μV for set size 22, but there was no further increase for set size 30 (8.23 μV).

Table 3. Mean FRP amplitude (in μV) at midline channels (Fz, Cz, Pz) in the time window between 380 and 480 ms after fixation onset for targets and distractors, respectively.

		Size 10	Size 22	Size 30
Targets	Fz	4.30 (4.87)	7.20 (5.10)	7.33 (4.83)
	Cz	5.05 (4.52)	7.66 (4.31)	8.04 (4.37)
	Pz	6.18 (3.63)	8.19 (3.51)	8.23 (4.07)
Distractors	Fz	1.04 (1.88)	0.66 (1.24)	0.29 (1.42)
	Cz	1.53 (1.90)	0.99 (1.27)	0.27 (1.49)
	Pz	2.62 (2.09)	1.31 (1.56)	0.44 (1.33)

Note: Numbers in parentheses denote SD.

Mean FRP amplitudes were compared with a 3 × 3 ANOVA for repeated measures with factors Set Size (10, 22, 30) and Channel (Fz, Cz, Pz). Results revealed a significant main effect Set Size (F(2,26) = 21.07, p < .001, η_p² = 0.62). Pairwise comparisons showed a significantly larger P300 amplitude for set sizes 22 and 30 as compared to set size 10 (ps < .001). The amplitude did not differ significantly between set sizes 22 and 30. Neither the main effect Channel nor the interaction Set Size × Channel was significant (Channel: F(1.06,13.80) = 2.18, p = .162; Set Size × Channel: F(1.97, 25.64) = 3.18, p = .059, see Table 3).

An earlier positive peak at a latency of ~250 ms was also present in the target FRPs. This early positivity was most prominent at mid-frontal electrode sites and its amplitude decreased towards posterior locations (Figure 2A). At location Fz, the amplitude was almost as high as the P300 amplitude but it was much smaller than the P300 at Pz. Importantly, this positivity did not vary with set size in this time range (Figure 2A).

Distractor FRPs

To corroborate our hypothesis that set size affects the response to targets specifically but not to distractors, we analyzed FRPs for distractors. These distractors were selected such that they were identical to the targets with respect to fixation rank and set size (see Methods for details). Grand average FRPs time-locked to the onset of fixation on the matched distractors for each set size are depicted in Figure 3A/B. Distractor fixations elicited a small positivity in the late time window (350-600 ms) but its amplitude was about four times lower than the respective wave elicited by targets (~2 vs. 9 μV). Overall, the distractor-related FRPs were similar between the set sizes at Fz and Cz. At location Pz, the amplitude for set size 10 was slightly higher than for the larger set sizes. However, this increase was noticeable already at around 100 ms post-fixation and remained throughout the epoch.

Figure 3.

A. Grand average FRPs time-locked to rank-matched distractor fixations for each set size on three midline channels (Fz, Cz, Pz). Time point zero denotes fixation onset. FRPs were baseline corrected using a baseline window of -200 to -100 ms prior to fixation onset. B. Topographical maps showing the mean amplitude at time points in steps of 50 ms.

For statistical analysis, we extracted the mean amplitude from distractor-FRPs in the same time window as used for the target analysis, for each set size and the three midline channels (Table 3). Mean FRP amplitudes were subjected to a 3 × 3 ANOVA for repeated measures with the factors Set Size (10, 22, 30) and Channel (Fz, Cz, Pz). The results showed significant main effects of Set Size (F(2,26) = 5.51, p =.010, η_p² = 0.30) and Channel (F(1.26,16.42) = 9.34, p <.001, η_p² = 0.42), and an interaction (F(2.20, 28.56) = 4.13, p =.024, η_p² = 0.24).

Pairwise comparisons regarding the main effect Set Size indicated a significantly larger amplitude for set size 10 than for set size 30 (ps =.007). Post-hoc tests for the factor Channel showed a significantly larger amplitude at Pz than at Fz and Cz. However, these differences were superseded by the interaction Set Size × Channel. The amplitude for set size 10 was significantly larger than for set size 30 on all channels (Fz: ps =.048, Cz and Pz: ps <.001). At location Pz, the amplitude decreased with increasing set size, that is, was larger for size 10 compared to set sizes 22 and 30 (ps < .001) and also differed between the latter (ps =.014). A channel difference was only found for set size 10 where the amplitude was significantly larger at Pz than at Cz and Fz (all ps < .001).

Control of confounding effects of eye movements

The analyzed FRP epochs differed with regard to eye movement characteristics such as number of fixations they contained and their durations, as well as saccade amplitudes. It is therefore important to show that the reported set size effects do not depend on systematic differences between these epochs. To that end, we categorized all epochs according to the number of fixations and saccades they contained. Figure 4 illustrates the most common category where the epoch contained two fixations (+1F and +2F) following the time-locking fixation F0 and corresponding saccades (+1S, +2S). The last event +2F starts within the epoch but exceeds the epoch limit, that is, it ends after +600 ms.

Figure 4.

Illustration of successive eye movements and the corresponding event coding in the FRP epochs for the most common case. The letter “F” denotes a fixation; “S” denotes a saccade. F0 stands for the time-locking event (either a target or rank-matched distractor fixation). Eye movements preceding the time-locking fixation are denoted with a minus sign, subsequent eye movements are denoted with a plus sign. The rectangular frame indicates the epoch duration.

We identified nine epoch categories which we defined by the eye movement event occurring last in the epoch. These categories are listed in Table S1, separately for each set size, and for targets and distractors. The percentage of epoch categories was comparable between set sizes. For both targets and distractors, the majority of epochs fell into category 5 (last event: +2F; 50.98 % and 70.93 %, respectively).

Varying fixation durations and saccade amplitudes can be confounded with effects of experimental conditions (Dimigen et al., 2011; Nikolaev et al., 2016). To control for eye movement effects, we statistically compared fixation durations and saccade amplitudes between set sizes. To limit the number of comparisons, we analyzed the eye movement characteristics for the six events that were most common: -1F, F0, +1F, and -1S, +1S, +2S. The preceding fixation (-1F) and saccade (-1S) were included as they potentially affect the baseline interval. Values for the eye movement characteristics were extracted from those epochs which contained the respective event for each set size, separately for target and distractor epochs. Fixation durations were only included if the respective fixation ended in the epoch. Table 4 shows the average fixation durations and saccade amplitudes for each set size.

Table 4.

Mean fixation durations of −1F, F0 and +1F fixations (in ms), and amplitudes of the corresponding saccades −1S, +1S, +2S (in degree v.a.) for each set size in target and distractor epochs, respectively. For each event, the ANOVA result for the comparison between set sizes is given.

	Targets				Distractors
Event	Size 10	Size 22	Size 30	F(2,26)	Size 10	Size 22	Size 30	F(2,26)
−1F	210 (25)	214 (19)	210 (22)	1.22	215 (26)	212 (24)	210 (22)	1.34
−1S	4.97 (0.55)	4.98 (0.59)	5.14 (0.59)	0.98	4.75 (0.55)	5.03 (0.59)	5.23 (0.64)	6.97 **
F0	250 (37)	256 (35)	247 (29)	2.96	220 (26)	216 (23)	217 (22)	1.15
+1S	5.25 (0.57)	5.42 (0.72)	5.47 (0.74)	1.34	5.27 (0.54)	5.83 (0.75)	5.82 (0.63)	6.54 **
+1F	214 (15)	214 (16)	216 (19)	0.16	206 (16)	203 (17)	205 (19)	0.74
+2S	4.12 (1.01)	4.41 (0.84)	4.59 (0.99)	4.80 *	4.77 (0.62)	4.71 (0.69)	5.25 (1.16)	3.19

Note: Numbers in parentheses denote SD

^* p < .05

^** p < 01.

A small percentage of epochs contained a third saccade (+3S, categories 6-9, Table S1). Given the small proportion of such cases, it is unlikely that the third saccade had an effect on the FRPs; therefore, it was not included in the analysis. Furthermore, the third saccades were located outside a time window used for the P300 analysis (Figure S1).

We compared the eye movement characteristics between set sizes (10, 22, 30) with a repeated measures ANOVA, separately for each characteristic for targets and for distractors. The results are presented in Table 4.

Target epochs: Durations of any of the -1F, F0, +1F fixations did not differ significantly between set sizes (Table 4). Saccade amplitudes of the different saccades comprised a comparatively small range (4.12-5.83°). -1S and +1S saccade amplitudes did not differ between set sizes. However, a significant effect of Set Size was found for the +2S saccade. Pairwise comparisons showed a significantly larger amplitude for set size 30 than size 10 (ps = .013). Critically, there was no difference in saccade amplitude between set size 10 and 22, yet the respective FRPs differed significantly. However, the +2S saccade occurred approximately at the time where we found the effect of set size on the P300 (~400 ms after fixation onset, Figure S1). To rule out any influence of saccade amplitude on this effect, we excluded epochs in which the +2S saccade was longer than 15°. In this case, +2S amplitudes did no longer differ between set sizes. Then, we repeated the main FRP analysis and observed the same pattern of the main statistical results (i.e., P300 was larger for set sizes 22 and 30 than for set size 10), as reported above (for details, see Supplementary Material).

Distractor epochs: As for target epochs, there were no differences between set sizes for any fixation durations (-1F, F0, +1F). Mean amplitudes of the +2S saccade also did not differ (Table 4). Significant differences were found for the -1S and +1S saccade amplitudes. Pairwise comparisons for -1S and +1S showed a significantly larger saccade amplitude for set size 22 and 30 than for set size 10, respectively (all p < .05). Analogous to the target control analysis, distractor epochs with -1S and +1S saccades longer than 15° were discarded. After this step, however, a significant difference in the +2S saccades occurred. Epochs with +2S outlier saccades (> 15°) were therefore also excluded. Thereafter, none of the saccade amplitudes differed between set sizes. The FRP analysis repeated for the reduced set of distractor epochs revealed almost identical results as the original analysis (for details, see Supplementary Material).

Discussion

In this study, we investigated the influence of target probability on the neural response to target detection in visual search with unconstrained eye movements. Target probability was manipulated by varying the set size (number of items in displays) in a multiple-target search, while EEG and eye movements were co-registered. Fixation-related potentials (FRPs) time-locked to first target fixations showed a prominent P300 component. The amplitude of this P300 was modulated by set size with a stronger response to targets in displays with a larger number of items and thus, decreased target probability. FRPs for distractors did not show activity consistent with a P300, and no increase of amplitude with set size. Our results suggest that set size specifically modulates activity evoked by targets but does not in the same way influence distractor-related activity.

Target FRPs

The detection of the target elicited a prominent positive component in the FRPs, resembling the characteristics of the P300 (see Kok, 2001; Polich, 2007; Polich, 2012, for reviews). The positive component occurred between 350-600 ms following fixation onset. This is in line with earlier studies demonstrating a late P300 in response to targets in free viewing (Devillez et al., 2015; Dias et al., 2013; Kamienkowski et al., 2012; Kaunitz et al., 2014; Ries et al., 2016; Touryan et al., 2017; Ušćumlić & Blankertz, 2016; Wenzel et al., 2016). The positive component started about 350 ms over mid-frontal electrode sites and shifted towards posterior locations with a centro-parietal maximum at around 450 ms, corresponding to the topography of the classical P300 or “P3b” (Polich, 2007). The amplitude increase from frontal to parietal sites was visible in the spatial maps (in particular from 450 ms onwards, Fig. 2B). This topographical effect did not reach significance in the statistical analysis of P300 amplitude on the midline channels. This can, however, be explained by the selection of the time window for statistical analysis. We used the same window for all electrodes and set sizes (centered around the average peak) which was relatively early (380-480 ms), and thus not ideally suited to highlight the frontal-to-parietal amplitude increase that was more prominent later in time. In the FRP control analysis, however, the effect of the anterior-to-parietal scalp topography was significant (see Supplementary Material).

Overall, the characteristics of the target-related positivity found in this experiment strongly support its interpretation as a P300, as suggested earlier (e.g., Devillez, Guyader, et al., 2015; Kamienkowski et al., 2012; Kaunitz et al., 2014; Wenzel et al., 2016). The detection of a target in visual search is a rare and task-relevant event. Stimulus probability and task-relevance are important factors that determine the P300 (for reviews see Kok, 2001; Picton, 1992; Polich, 2012). These factors likely underlie the distinct response to the target fixations which was considerably different from the response to the distractor fixations. This observation is in accordance with previous studies which have demonstrated that FRP components discriminate between target and distractor fixations in free viewing (Devillez et al., 2015; Dias et al., 2013; Kamienkowski et al., 2012; Kaunitz et al., 2014; Ries et al., 2016; Touryan et al., 2017; Ušćumlić & Blankertz, 2016; Wenzel et al., 2016). The current study extends those findings by showing that the response to the target fixations depends on set size, and thus on target probability.

In line with our hypothesis, the results revealed a modulation of the target-related P300 by set size. A larger P300 amplitude was found for set sizes 22 and 30 as compared to set size 10. Notably, the FRPs did not differ up until this late positivity, indicating that set size influenced higher-order cognitive processes associated with late FRP components while not affecting early sensory visual processing. P300 topography was comparable between set sizes with the maximum amplitude over centro-parietal sites, suggesting that it was the same component, only altered in magnitude by the set size manipulation. On the three analyzed midline channels, the amplitude of the P300 was significantly larger for set sizes 22 and 30 than for set size 10. It is well known that the amplitude of the P300 increases as target probability decreases (Duncan-Johnson & Donchin, 1977, 1982; Polich & Bondurant, 1997; Polich et al., 1991). The P300 amplitude has been shown to be sensitive to global probability, local probability and stimulus sequence structure (Duncan-Johnson & Donchin, 1977, 1982, Gonsalvez et al., 1995, 1999; Polich & Bondurant, 1997; Polich et al., 1991; Squires et al., 1977, 1976). In the current experiment, with increasing set size, more distractors were added to the displays, rendering the target a rarer stimulus among them. As a consequence, the target fixation rank and time until target detection increased as a function of set size. In 10-item displays, the target was found, on average, after 6.08 fixations, in 22-item displays after 10.96 fixations, and in 30-item displays after 15.09 fixations. This increase of the target fixation rank (i.e., a larger number of distractor fixations preceding the target) was associated with a decreased target probability, providing the basis for the larger P300 amplitude in response to targets in the larger set size displays.

Our results are in line with the findings of Luck and Hillyard (1990) from a covert search task. The authors observed an increase of P300 amplitude with set size in target-present trials in ERPs. In their experiment, set size affected P300 amplitude in serial but not in parallel search, suggesting that the serial processing of the stimuli and resulting local probability plays an important role for the modulation of the P300 in visual search. To our knowledge, the current study is the first demonstrating a similar dependence of the P300 on probability of a target during free viewing visual search.

There was no further increase in amplitude from size 22 to size 30. One possible explanation is that the increase in set size between displays decreased (12 items vs. 8 items), which may have reduced a potential difference in the corresponding P300 amplitudes between the large set sizes. Another related aspect is the fixation rank. Although the average fixation ranks systematically differed between the set sizes and increased with a similar rate, a closer inspection of the fixation rank distributions showed a greater variability of the ranks in searches of 22- and 30-item displays (see also Table 2). While the set size 10 contained almost exclusively low-rank targets (rank < 15), the larger set sizes both contained a substantial number of medium-rank targets (in the range of 15-25). The higher variability of the fixation rank might have attenuated an amplitude difference in the averaged FRPs.

We also observed an earlier positivity between 200-300 ms following fixation onset in the FRPs. This positive wave did not vary with set size but was larger for targets than for distractors. This effect should be interpreted with caution because eye movement characteristics were not matched between targets and distractors. However, it seems unlikely that eye movements alone explain this difference. The positivity reached its peak at a latency of ~250 ms and was most pronounced over the mid-frontal areas. These properties are similar to those of the P2 component in visual ERPs, which has been associated with stimulus categorization and selective attention (Kotchoubey, 2006; Luck, 2014; Potts, 2004; Potts, Patel, & Azzam, 2004). In visual target detection (oddball) tasks, the anterior P2 (P2a) has been shown to be larger for rare targets than frequent standards (or distractors), in particular for task-relevant targets that required an overt or covert response (Potts, 2004; Potts & Tucker, 2001). Furthermore, the P2a was found to be enhanced for stimuli designated as targets (“instructed targets”) independent of stimulus frequency and response mode (Potts et al., 2004). The authors have argued that the P2a is an index of higher-order operations in the frontal cortex evaluating the task-relevance of stimuli which interacts with perceptual processes in posterior brain areas (Potts, 2004; Potts, Martin, Burton, & Montague, 2006; Potts et al., 2004). It is therefore possible that the early positivity observed in the current experiment reflects a P2a.

Distractor FRPs

To validate that set size specifically influences the neural response to targets but not to distractors, we analyzed a subset of distractor fixations matched to the targets with regards to set size and fixation rank. According to the FRP results, the rank-matched distractor fixations did not elicit EEG activity compatible with a P300. We observed a small positive deflection in the distractor FRPs in the time range of the P300 but its amplitude was small (highest peak ~2.5 μV). It was also noticeable that this peak only marginally exceeded earlier peaks in the epochs which coincided with the onsets of saccades (discussed in more detail below). This result greatly differed from the pronounced effects found for the target fixations, which evoked a large P300 with peak amplitudes ranging up to around 9 μV.

When comparing the distractor-FRPs between set sizes, however, a significant effect on mean FRP amplitude was found (380-480 ms). For set size 10, the amplitude was slightly increased for the three midline channels, differing from the other set sizes mainly at Pz. The distractor amplitudes for set size 10 were enhanced as early as ~100 ms post-fixation which is incompatible with the temporal specificity of a P300. This was different from the targets where the revealed set size modulation was specifically associated with the P300 in the late time window. Beyond that, visual inspection of distractor FRP scalp maps showed that the set size difference occurred over the posterior cortex (parieto-occipital sites), unlikely reflecting P300 activity. Thus, we refrain from further interpretation of the effect as it was small and did not seem to reflect a distinct FRP component.

Our observations are in line with earlier FRP studies where no P300-like component has been found for distractors (e.g., Brouwer et al., 2013; Devillez et al., 2015; Dias et al., 2013; Finke et al., 2016; Kamienkowski et al., 2012; Kaunitz et al., 2014; Ries et al., 2016; Ušćumlić & Blankertz, 2016; Wenzel et al., 2016). In oddball tasks, distractors typically do not elicit a P300, unless they are novel or infrequent (Comerchero & Polich, 1999; Polich, 2007; Polich & Comerchero, 2003). Importantly, the analysis of the distractors also served as a control to preclude the possibility that the fixation rank alone could explain the modulation of the target-related P300. Due to the matching procedure, the fixation rank of the distractors increased with set size in the same systematic fashion as for the targets. The absence of a (P300) amplitude increase with set size in the distractor FRPs therefore shows that the mere passage of time and increase of fixation rank does not result in a larger P300. This finding corroborates that the increase of P300 amplitude observed for target fixations originated from the modulation of target probability. In covert serial search, Luck and Hillyard (1990) did not find a dependence of P300 amplitude in target-absent trials where only distractor items were processed. Our results from serial search with eye movements are in line with their findings, showing that P300 amplitude increases with set size only for task-relevant targets but not for task-irrelevant distractors.

Control of Confounding Effects of Eye Movements

To obtain reliable FRP components we followed a rigorous methodology in this study. We applied independent component analysis (ICA) to correct ocular artifacts, defined strict criteria for the selection of fixation events for FRP analysis, and conducted a comprehensive control analysis to ensure that eye movements cannot explain the results.

ICA is a powerful tool to remove oculomotor artifacts from EEG data (Jung, Makeig, Humphries, et al., 2000; Jung, Makeig, Westerfield, et al., 2000) and has become state-of-the art in free viewing studies (e.g., Devillez, Guyader, et al., 2015; Jangraw et al., 2014; Ries et al., 2016; Simola et al., 2015; Touryan et al., 2017). We applied the variance ratio criterion (Plöchl et al., 2012), which allows for objective identification of ocular components based on integrated information from the eye tracker. Plöchl et al. (2012) have shown that, following this approach, ICA eliminates corneo-retinal dipole and eyelid artifacts, and considerably reduces saccadic spike activity. However, the latter was not entirely removed by ICA in their study. We found that the three consecutive peaks in both the target- and distractor-FRPs coincided with the onsets of sequential saccades (Figure S1), possibly reflecting such residual oculomotor activity. The analysis discussed next ensured, however, that the interpretation of FRPs was not compromised by such possible distortions.

We conducted an extensive control analysis to rule out that our findings could be attributed to differences in eye movements. A pivotal aspect in the analysis of FRPs obtained during free viewing is the temporal overlap of brain activity evoked by subsequent eye movements (Dandekar et al., 2012; Dias et al., 2013; Dimigen et al., 2011; Kristensen, Guerin-Dugué, & Rivet, 2017; Nikolaev et al., 2016). This can result in distortions of the evoked potential of interest and affects in particular the late FRP components, such as the 1P300 or N400 (Dandekar et al., 2012; Dias et al., 2013; Dimigen et al., 2011; Kristensen et al., 2017). Researchers have therefore attempted to obtain long fixations by imposing limitations on oculomotor behavior in their experiments, such as training participants to make long fixations (Kaunitz et al., 2014) or guiding search in structured tasks (Brouwer et al., 2017, 2013; Ries et al., 2016; Touryan et al., 2017). In the current study, participants were allowed to move their eyes freely without any constraints. This resulted in fixations with an average duration of around 200-250 ms, which is typical for letter search tasks (Körner et al., 2014). Consequently, there was overlap of the P300 with subsequent neural responses. It was therefore important to control, on the one hand, the degree of temporal overlap depending on fixation durations, and, on the other hand, saccade amplitudes which correlate with the magnitude of the saccadic spike potential and lambda response (Dimigen et al., 2011; Kaunitz et al., 2014; Keren et al., 2010; Nikolaev et al., 2016; Plöchl et al., 2012).

Up to now, the overlap problem has been addressed by approaches such as linear regression (Dandekaret et al., 2012; Dias et al., 2013; Kristensen et al., 2017), subspace subtraction (Dias et al., 2013), or matching of eye movement characteristics (Devillez et al., 2015; Dias et al., 2013; Dimigen et al., 2011; Kamienkowski et al., 2012; Nikolaev et al., 2016). We adopted an approach similar to the latter, where we balanced possible distortions between the set sizes. To this end, we statistically compared fixation durations and saccade amplitudes of consecutive eye movements that occurred in the EEG epochs between the set sizes for targets and distractors. In contrast to earlier studies (e.g., Brouwer et al., 2013; Kamienkowski et al., 2012; Nikolaev et al., 2011; Ries et al., 2016), the duration of an EEG epoch was not equal to the preset minimal fixation duration. Consequently, the number of consecutive eye movements per epoch varied. To account for this variation, we categorized all epochs depending on the number of eye movements and calculated the percentages of the resulting categories. The analysis showed comparable proportions of the categories for the three set sizes, indicating that the number of subsequent eye movement events potentially affecting the FRPs did not differ systematically. It also allowed us to identify the critical eye movement events for which we then compared and – where necessary – balanced the corresponding characteristics between conditions.

We did not observe any differences in the fixation durations between set sizes, neither in the target nor in the distractor epochs. This precludes the possibility that the modulation of the P300 amplitude by set size resulted from a varying degree of overlap with adjacent neural responses. The results further affirmed that the baseline did not contain differential activity from the preceding fixation. Noteworthy, fixations on targets were consistently longer than on distractors, a common finding in visual search that highlights the prominent role of target processing (e.g., Brouwer et al., 2017; Körner et al., 2014; Meghanathan, van Leeuwen, & Nikolaev, 2015). These systematic differences hamper, however, a direct comparison of the target- and distractor-FRPs, which is why we instead focused on the comparison of FRPs between set sizes separately for each item type. Regarding the analyzed saccade amplitudes, we could successfully eliminate initial differences by removing epochs with outlier saccades. Control FRP analyses with datasets where all eye movement characteristics were comparable between set sizes confirmed the original FRP results for targets and distractors.

Finally, the selection of a suitable baseline is a challenge in co-registration because there is no “clean” interval where background activity is uniformly distributed (for details, see Nikolaev et al., 2016). We selected an interval that preceded saccade onset (-200 to -100 ms) and was therefore not contaminated by saccadic activity. This is a common choice in FRP research (Kamienkowski et al., 2012; Kaunitz et al., 2014; Ries et al., 2016; Simola et al., 2013). In the saccade onset distributions (Figure S1), one can see that the saccades preceding the fixation of interest (−1S, see Figure 4 for the notation) occurred between -100 to 0 ms before the onset of that fixation. Since a varying degree of temporal overlap with the previous fixation can also produce differences in baseline activity, we further ensured that the duration of the previous fixation was equal between set sizes (-1F, Table 4). Altogether, these aspects speak against a bias in baseline activity affecting the estimation of FRP amplitude. As additional control, we re-analyzed the data using an alternative baseline from 0 to +20 ms. Such a post-fixation baseline is both free of saccadic and visual activity and has been used previously (Hutzler et al., 2007; Rämä & Baccino, 2010; Simola et al., 2015). The analysis yielded virtually identical results for targets, revealing the same effect of set size on P300 amplitude. For distractors, we observed minor changes in FRP amplitudes and statistical results for some pairwise comparisons in post-hoc testing, but those did not alter the overall pattern of results. Hence, these control analyses demonstrate that our findings are robust against different baseline corrections.

Taken together, these efforts substantiate our findings and rule out the possibility that the modulation of P300 amplitude by set size can be accounted for by eye movements.

Conclusion

This work supports the view that the P300 component of the fixation-related potential is a neural correlate of target processing in free-viewing visual search. We show for the first time that this fixation-related P300 depends on target probability, manipulated in the current experiment by varying the set size of displays in an overt visual search task. The detection of a target elicited a stronger P300 when preceded by a larger number of distractor fixations. For distractors, we did not observe such a modulation of amplitude and no activity resembling a P300. This suggests that set size, and thus probability, specifically affects target but not distractor processing. In conclusion, our findings highlight that target probability is a fundamental determinant of the P300 in visual search.